Systematic design of advanced control structures€¦ · 2 MVs 2 CVs. 26 Design procedure for...

Systematic design of

advanced control structures

Adriana Reyes-Lúa

February 28th, 2020

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Content

• Motivation and scope

• Active constraint switching with advanced control structures (chapter 2)

– Case study: mixing

– Case study: distillation column

– Case study: cooling cycle (chapter 3)

– Case study: cooler (chapter 4)

• MV to MV constraint switching

– Split range control

• Design of standard split range controllers (chapter 5)

• Generalized split range controller (chapter 6)

– Multiple controllers with different setpoints (chapter 7)

• Improved PI control for tank level (chapter 8)

• Conclusions

3

Motivation and scope

4


CV: controlled

variable (output, y)• Temperature

• Pressure

• Concentration

5


CV: controlled


• Pressure

• Concentration

MV: manipulated

variable (input, u)• Valve opening

• Compressor rotational

speed

6


CV: controlled


• Pressure

• Concentration

MV: manipulated



speed

DV: disturbance variable (d)• Ambient temperature

• Raw materials

• Desired production

7


CV: controlled


• Pressure

• Concentration

MV: manipulated



speed

DV: disturbance variable (d)• Ambient temperature

• Raw materials

• Desired production

8


9


Top-down analysis:S1-S4: Identify steady-state

optimal operation

Bottom-up analysis:S5-S7: Design control

structure

10


Bottom-up analysis:S5: regulatory control layer

11



S6: supervisory control layer

S7: online optimization layer

12





13





Keeps operation

in the right

active constraint region

14


Constraint region«region in the disturbance

space defined by which

constraints are active within it»

Disturbance 1

Dis

turb

an

ce

2

Jacobsen and Skogestad (2011) Active constraint regions for optimal operation of chemical processes. Industrial & Engineering Chemistry Research.


15

Motivation and scopeS6: supervisory control layer

16


Model predictive control


Cost

Model

Constraints

17


Model predictive control

Advanced control structures


18

Active constraint switching with classical advanced

control structures

Figure taken from www.transmittershop.com/blog/causes-solutions-annoying-noise-control-valves

19


control structures


20


control structures


21

Design procedure for active constraint switching with

classical advanced control structures

A1• Define control objectives, CV constraints and MV constraints

A2• Organize constraints in priority list

A3• Identify possible and relevant active constraint switches

A4• Design control structure for optimal operation

A5• Design control structure to handle active constraint switches

22

Design procedure for active constraint switching

Case study:Mixing of

air and MeOH

24


Step A1: Define control objectives, CV constraints and MV constraints

25



2 CVs2 MVs

26



Control objectives:• Keep y1 = xMeOH = 0.10 ideal

• Keep y1 =xMeOH > 0.08

• Control y2 = mtot ideal

2 CVs2 MVs

27


Control objectives:• Keep y1 = xMeOH = 0.10

• Keep y1 =xMeOH > 0.08

• Control y2 = mtot

2 CVs2 MVs

u1 is has a maximum value


28


Step A2: Organize constraints in priority list

Figure from www.indelac.com/blog/control-valves-vs.-regulators-in-control-applications

29


Step A2: Organize constraints in priority list

• Constraint on air flow (u1)

• Constraint on MeOH flow (u2)(P1) Physical MV inequality constraints

• Constraint (max and min) on xMeOH (y1)(P2) Critical CV inequality constraints

• Setpoint on xMeOH (y1)(P3) Less critical CV and MV constraints

• Setpoint on mtot (y2)(P4) Desired throughput

• No unconstrained degrees of freedom(P5) Self-optimizing variables

30


Step A3: Identify possible and relevant active constraint switches

31



• Case 1: CV to CV constraint switching

One MV switching between two alternative CVs.

32



Split range control

Valve position control

Different controllers

with different setpoints

• Case 2: MV to MV constraint switching

More than one MV for one CV.

33



• Case 3: MV to CV constraint switching

MV controlling a CV that may saturate; no extra MVs

Input saturation pairing rule«an MV that is likely to saturate at

steady-state should be paired with a

CV that can be given up»

Low priority CVHigh priority CV:

always controlled

MV that does not

saturate

34



• Case 3: MV to CV constraint switching

MV controlling a CV that may saturate; no extra MVs

Following input

saturation pairing rule

NOT following input


35



• At nominal operation point all

constraints are satisfied

• Constraint switch:

• Reach maximum air flow (u1)

• Lose a degree of freedom (case 3)• Must give up controlling the

constraint with the lowest priority

(desired throughput)

36


Step A4: Design control structure for optimal operation

37



Following input


Case A

Low

priority

CV

MV likely to saturate

38



Case A Case B

NOT following input


Following input


Low

priority

CV


High

priority CV

not always

controlled


39



Case A Case B

NOT following input


Following input


Needs MV to CV

switching

40


Step A5: Design control structure to handle active constraint switches

41


Step A5: Design control structure to handle active constraint switches

Case B-SRC

Split range control+selector

Case B-VPC

Valve position control + selector

42


Case study: Mixing of air and MeOHMV1 is saturated:

lost degree of freedomHigh priority CV: concentration

Low priority CV (throughput) MV2 is not saturated:

It should be used to control the high priority CV

43

MV to MV constraint switching

Split range control Different controllers with

different setpoints

Valve position

control

44

Classical split range control

Monogram of Instruments and Process Control

prepared at Cornell, NY, in 1945

CV

MV1

MV2

Eckman, D.P. (1945).

Principles of industrial

control, New York.

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v internal signal to split range block limited physical meaning

v* split value

ui controller output physical meaning

αi gain from v to ui slope

47



v* split value degree of freedom



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v* split value degree of freedom



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Design of split range control: select slopes

Goal: get desired loop gain |g C|

at crossover frequency

51




52




Fast process Slow process

Desired

gain for ui

Common

gain in C

DOFDesired

gain for ui

Common

gain in C

DOF

53

Design of split range control: order of MVs

Define the desired operating point for every MV

Group the MVs according to the effect on the CV

Within each group, define order of use

55

Design of split range control

u1 = uAC : air conditioning (AC)

u2 = uCW : cooling water (CW)

u3 = uHW : heating water (HW)

u4 = uEH : electrical heating (EH)

56

Classical split range control: a compromise

1 DOF

2 tuning parameters

57

Generalized split range controller

58


Preliminary step:

• Define order of use of MVs ( j=1,…,N)

• Tune controllers

59


«Baton strategy» logic

k is the active input

• Ck computes uk’ (suggested value for uk)

• If ukmin< uk’< uk

max

• Keep uk active and uk uk’

• Keep remaining ui at limiting value

• else

• Set uk= ukmin or uk< uk

max, depending on the reached limit

• New active input selected according to predefined sequence

(j= k-1 or j=k+1)Preliminary step:


• Tune controllers

60


«Baton strategy» logic

k is the active input

• Ck computes uk’ (suggested value for uk)

• If ukmin< uk’< uk

max

• Keep uk active and uk uk’

• Keep remaining ui at limiting value

• else

• Set uk= ukmin or uk< uk

max, depending on the reached limit

• New active input selected according to predefined sequence

(j= k-1 or j=k+1)Preliminary step:


• Tune controllers The active input will decide when to switch and

will remain active as long as it is not saturated.

61


u1 = uAC : air conditioning (AC)

u2 = uCW : cooling water (CW)

u3 = uHW : heating water (HW)

u4 = uEH : electrical heating (EH)

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Generalized vs standard split range controller

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Generalized split range controller: initialization

How to

start?

k

64


How to

start?

This suggested input was

not being applied while

input k was not in use

This accumulated error is

not due to the previous

actions of input kk

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Resetting:Only use error

when I receive

the baton

Initial action proportional to error at tb

k

66


Back-calculation:

I was keeping

track of the

applied input

67


Resetting:

Back-calculation:

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Generalized split range controller vs MPC

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Multiple controllers with different setpoints

Does this make sense at any point?

70

Multiple controllers with different setpoints

Setpoint

deviation

Input

usage

71

Multiple controllers with different setpoints:

Optimal setpoint deviation

Linear for u and quadratic for Δy Inputs are a linear function of output

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Linear for u and quadratic for Δy Inputs are a linear function of output

Cost when using uk as input

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Linear for u and quadratic for Δy

Optimal

setpoint deviation

minimizing cost

Inputs are a linear function of output

Cost when using uk as input

74

Multiple controllers with different setpoints: Case study

QAC : air conditioning

QHW : heating water

QEH : electrical heating

75


Cost: linear for u and quadratic for Δy


QHW : heating water


76




QHW : heating water


Inputs (Qi) are a linear function of output (T)

77

Multiple controllers with different setpoints: Room T



QHW : heating water


Inputs (Qi) are a linear function of output (T)

Optimal setpoint deviation minimizing cost

78



QHW : heating water


Optimal setpoint

deviation

minimizing cost

79


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Lower accumulated

cost with minimum

setpoint deviation

Constant setpoint

81

Final comments

• Steady-state optimal operation may be easily achieved using PID-based

control structures– Chapters 2,3,4: active constraint switching

– Chapter 7: optimal setpoints

82

Final comments




• Useful to systematically define control objectives, feasibility and tools– Priority list of constraints

– Control structures available for each type of switch (CV-CV, MV-MV, MV-CV)

83

Final comments




• Useful to systematically define control objectives, feasibility and tools– Priority list of constraints

– Control structures available for each type of switch (CV-CV, MV-MV, MV-CV)

• Possible to improve performance of PID-based advanced control– Chapters 5, 6: design of split range controllers

– Chapter 8: improved level control

84

One final comment

• The “gap” between theory and practice can be in both directions

Åström, K. J., & Kumar, P. R. (2014). Control: A perspective. Automatica, 50(1), 3–43.

Centrifugal governor used in steam

engines in the 1780’s:

Proportionally controls fuel flow to

maintain engine speed.

Theoretical investigation started about

a century later.speed

fuel

Systematic design of

advanced control structures

Thank you for your attention!

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Systematic design of advanced control structures€¦ · 2 MVs 2 CVs. 26 Design procedure for...

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